Physics of Speed Detection

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Speed detection is one of the most notorious functions of our local and state police. How do they know how fast we are going? Speed determination is accomplished in two basic ways. First, the least sophisticated method is dependent upon an officer's ability to guess your speed. Second, either some electronic method using radar or laser instrumentation authenticates that officer's guess. As you will see, their guesses are usually right on target.

What does this mean for you? Usually a speeding ticket or if your infraction isn't a flagrant disregard for safety, a friendly warning.

Speed(s) is the distance travelled divided by the total time it took to get from the starting point to the ending point, or:

s=(Dx)/(Dt)

How does the speedometer work?

Your vehicle's speedometer determines your speed by examining the angular velocity(v) of your axle (how fast your axle spins) and multiplying it with the manufacturers' recommended circumference for the vehicle's tires. (This is why using oversize tires will cause your speedometer to register a lower speed than your actual travelling speed-the circumference of the oversize tires is greater than that of the recommended tires, while the angular speed remains the same) So, in application:

s = v*2pr

Why should we limit our speed?

Speed limits are designated for roads based on the roads characteristics such as its geometry and capacity, and traffic characteristics such as overall volume, hourly volume and traffic density. Speed limits are designed to most effectively and safely regulate traffic.

There are several methods of manual speed detection, but they are all based on obtaining a known distance and comparing it to the time it took to travel that distance. Officers who have been watching traffic for a long time tend to get a really good grasp of almost instantaneously knowing how fast vehicles are travelling. A table showing an officer's guess along side an inexperienced observer's guesses and the radar results is shown below. Note that Officer Keeler's guesses are all within 3 mph of the actual speed. My guesses tend to have a higher deviation and were sometimes influenced by officer Keeler's guesses if he spoke first.

The other methods include using a stopwatch and timing a vehicle on a known distance, either from the ground or in an aircraft, and pacing a vehicle. Pacing a vehicle involves either matching speeds with the vehicle and checking your speedometer or locating distinct markings and counting so that you can again divide distance by time to obtain a speed.

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